Sometimes there are two complete thoughts in a sentence that go well together, but the chemistry doesn't seem quite right. Their future together seems shaky. Getting joined in one sentence by a comma would be going too fast. On the other hand, breaking the thoughts into two separate, complete sentences seems rash.

Thankfully, the semicolon (;) provides help to thoughts that aren't ready for a comma, but certainly don't want to be broken up. Putting it in grammatical terms, "The UPI Stylebook and Guide to Newswriting" says, "the semicolon is used to indicate a greater separation of thought and information than a comma can convey, but less than the separation that a period/full stop implies."

According to the "Bloomsbury Grammar Guide" by Gordon Jarvie, the semicolon serves two primary functions within a sentence. It is used as an alternative to conjunctions (avoiding overuse of words such as 'and,' 'but,' 'for'), and it can be used to help clarify complex lists.

When it comes to eliminating extra conjunctions between two independent thoughts or clauses, the "Gregg Reference Manual" encourages use of a semicolon, not a comma.

Let's take the use of the conjunction but. We could include the word and it would be fine in this sentence:

Most of the board members approved the sale of the company, but the management and employees did not.

Certainly fine, but if we want something a bit more punchy, we can take out the but and replace it with a semicolon:

Most of the board members approved the sale of the company; the management and employees did not.

Semicolons can also set one clause off from another with the added help of a transitional word or phrase. Examples of transitional expressions include:

accordingly

however

so

besides

moreover

that is

consequently

namely

then

for example

nevertheless

therefore

furthermore

on the contrary

thus

hence

otherwise

yet

Let's use a transitional word in the example sentence we've been using to see semicolon in action.

Most of the board members approved the sale of the company; nevertheless, the management and employees did not.

Those are the ways a semicolon can keep clauses together in a sentence.
The other use of semicolon can be used to clean up items in a series. Let's take our example sentence, put a positive spin on it and set it to work in a series, like so:

Rather than sell the company, the board opted instead to open new offices in Tokyo, Japan; Paris, France; Perugia, Italy; and Slough, England.

Comma after comma in a sentence like that could be confusing, but semicolon maintains the list-like properties of the series while providing just the right amount of division.

And here's a nice and easy rule regarding semicolons: in the event quotation marks are used adjacent to a semicolon, the quotation marks always appear before the semicolon. That rule is the same in both Standard English and American English.
In the end, breaking up sentences can be hard to do. Fortunately, loveor at least, semicolonkeeps them together.